Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e...

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Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

Transcript of Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e...

Page 1: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–1 Application of commutative law of addition.

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Page 2: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–2 Application of commutative law of multiplication.

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Page 3: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–3 Application of associative law of addition. Open file F04-03 to verify.

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Page 4: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–4 Application of associative law of multiplication. Open file F04-04 to verify.

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Page 5: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–5 Application of distributive law. Open file F04-05 to verify.

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Page 6: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–6

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Page 7: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–7

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Page 8: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–8

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Page 9: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–9

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Page 10: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–10

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Page 11: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–11

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Page 12: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–12

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Page 13: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–13

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Page 14: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–14

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Page 15: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–15 Gate equivalencies and the corresponding truth tables that illustrate DeMorgan’s theorems. Notice the equality of the two output columns in each table. This shows that the equivalent gates perform the same logic function.

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Page 16: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–16 A logic circuit showing the development of the Boolean expression for the output.

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Page 17: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–17 Gate circuits for Example 4–8. Open file F04-17 to verify equivalency.

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Page 18: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–18 Implementation of the SOP expression AB + BCD + AC.

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Page 19: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–19 This NAND/NAND implementation is equivalent to the AND/OR in Figure 4–18.

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Page 20: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–20 Implementation of the POS expression (A + B)(B + C + D)(A + C).

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Page 21: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–21 A 3-variable Karnaugh map showing product terms.

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Page 22: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–22 A 4-variable Karnaugh map.

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Page 23: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–23 Adjacent cells on a Karnaugh map are those that differ by only one variable. Arrows point between adjacent cells.

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Page 24: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–24 Example of mapping a standard SOP expression.

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Page 25: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–25

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Page 26: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–26

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Page 27: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–27

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Page 28: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–28

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Page 29: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–29

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Page 30: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–30

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Page 31: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–31

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Page 32: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–32

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Page 33: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–33

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Page 34: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–34

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Page 35: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–35 Example of mapping directly from a truth table to a Karnaugh map.

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Page 36: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–36 Example of the use of “don’t care” conditions to simplify an expression.

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Page 37: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–37 Example of mapping a standard POS expression.

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Page 38: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–38

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Page 39: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–39

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Page 40: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–40

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Page 41: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–41

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Page 42: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–42 A 5-variable Karnaugh map.

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Page 43: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–43 Illustration of groupings of 1s in adjacent cells of a 5-variable map.

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Page 44: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–44

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Page 45: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–45 A VHDL program for a 2-input AND gate.

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Page 46: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–46

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Page 47: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–47 Seven-segment display format showing arrangement of segments.

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Page 48: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–48 Display of decimal digits with a 7-segment device.

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Page 49: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–49 Arrangements of 7-segment LED displays.

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Page 50: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–50 Block diagram of 7-segment logic and display.

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Page 51: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–51 Karnaugh map minimization of the segment-a logic expression.

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Page 52: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–52 The minimum logic implementation for segment a of the 7-segment display.

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Page 53: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–53

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Page 54: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–54

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Page 55: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–55

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Page 56: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–56

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Page 57: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–57

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Page 58: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–58

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Page 59: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure 4–59

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Figure 4–60

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Figure 4–61

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Figure 4–62

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Figure 4–63

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Figure 4–64

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Figure 4–65

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Figure 4–66

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